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Bartlett's formula for a general class of nonlinear processes

  • Christian Francq
  • Jean-Michel Zakoïan

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear processes, involving only the autocorrelation function of the observed process. The second term, which is specific to nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of the linear innovation process and the autocorrelation function of its square. This formula is obtained under a symmetry assumption on the linear innovation process. It is illustrated on ARMA-GARCH models and compared to the standard formula. An empirical application on financial time series is proposed. Copyright 2009 Blackwell Publishing Ltd

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Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 30 (2009)
Issue (Month): 4 (07)
Pages: 449-465

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Handle: RePEc:bla:jtsera:v:30:y:2009:i:4:p:449-465
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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  3. Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers 2008-05, Centre de Recherche en Economie et Statistique.
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